U.S. Pat. Nos. 5,308,974 and 5,418,363 issued to Elings et al. disclose a method in which a first scan to obtain the topography of a sample surface is used to guide a subsequent second scan for some other task related to the topography. As is standard in SPM applications, this topography represents a simple false surface of the object that is a function (i.e., there is only one z coordinate value for each pair of x,y coordinate values) when in fact the true surface of the object may be a complex surface that is a non-function (i.e. for at least one pair of x,y coordinate values, there is more then one z coordinate value). In other words, the topography is itself a function. The second scan is then performed along the topography, along a fixed (i.e., constant) offset of the topography, or along a function of the topography. However, such an approach is inadequate and inappropriate for use in SPM applications, such as nanomachining and the dynamic measurement of induced parametric change.
In particular, in nanomachining it is the complex desired surface which is the target not the pre-existing topography. Indeed, simple mathematical considerations demonstrate that simply adding or subtracting a fixed amount from an original topography can only reproduce the topography.
Furthermore, in nanomachining and other SPM operations, it is often necessary to perform an operation on an object or a surface or subsurface structure of the object that has a true surface or volume which is not a function. However, such a true surface or volume can never be accurately scanned by a simple offset from the true surface or volume because complex back and forth or in and out motions are required to accurately follow the true surface or volume.